KTH Royal Institute of Technology and Scania are entering the GCDC 2011 under the name Scoop –Stockholm Cooperative Driving. This paper is an introduction to their team and to the technical approach theyare using in their prototype system for GCDC 2011.

We study the fundamental relationship between two relevant quantities in compressive sensing: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/ log n (m being the number of measurements and n the dimension of the sparse signal), and the mean square estimation error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total signal power when the sparsity level is fixed. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean square error. This tradeoff is achievable using a two-step approach: first support set recovery, then estimation of the active components. Finally, for both deterministic and random signals, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery.

For compressive sensing, we derive achievable performance guarantees for recovering partial support sets of sparse vectors. The guarantees are determined in terms of the fraction of signal power to be detected and the measurement rate, defined as a relation between the dimensions of the measurement matrix. Based on this result we derive a tradeoff between the measurement rate and the mean square error, and illustrate it by a numerical example.

The article starts by examining the idea of conservation laws as applied to market economies. It formulates a measure of financial entropy and gives numerical simula-tions indicating that this tends to rise. We discuss an analogue for free energy released during this process. The concepts of real and symbolic appropriation are introduced as a means to analyse debt and taxation. We then examine the conflict between the conservation laws that apply to commodity exchange with the exponential growth implied by capital accumulation and how these have necessitated a sequence of evolutionary forms for money, and go on to present a simple stochastic model for the formation of rates of interest and a model for the time evolution of the rate of profit.

In this letter we develop a solution for decentralized localization of transceiving nodes in wireless networks. By exploiting a common transmission schedule, this is achieved without any additional communication and dispels the need for synchronized nodes. We derive the Cramer-Rao bounds for the solution and formulate two practical estimators for localization. Finally, the solution and estimators are tested in numerical experiments.

Suppose a linear model Y = Hx+n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix so as to minimize the mean square error (MSE) when estimating x from . This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed H, the minimum MSE (MMSE) has no analytical form. Secondly, theMMSE is generally not convex in . Thirdly, derivatives of the MMSEw.r.t. are hard to obtain. This paper casts theproblemas a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy-markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why.

Suppose a vector of observations y = Hx + n stems from independent inputs x and n, both of which are Gaussian Mixture (GM) distributed, and that H is a fixed and known matrix. This work focuses on the design of a precoding matrix, F, such that the model modifies to z = HFx + n. The goal is to design F such that the mean square error (MSE) when estimating x from z is smaller than when estimating x from y. We do this under the restriction E[(Fx)TFx] ≤ PT, that is, the precoder cannot exceed an average power constraint. Although the minimum mean square error (MMSE) estimator, for any fixed F, has a closed form, the MMSE does not under these settings. This complicates the design of F. We investigate the effect of two different precoders, when used in conjunction with the MMSE estimator. The first is the linear MMSE (LMMSE) precoder. This precoder will be mismatched to the MMSE estimator, unless x and n are purely Gaussian variates. We find that it may provide MMSE gains in some setting, but be harmful in others. Because the LMMSE precoder is particularly simple to obtain, it should nevertheless be considered. The second precoder we investigate, is derived as the solution to a stochastic optimization problem, where the objective is to minimize the MMSE. As such, this precoder is matched to the MMSE estimator. It is derived using the KieferWolfowitz algorithm, which moves iteratively from an initially chosen F0 to a local minimizer F*. Simulations indicate that the resulting precoder has promising performance.

We introduce a method to improve performance of multiple-description coding based on legacy video coders with pre- and postprocessing. The pre- and post-processing setup is general, making the method applicable to most legacy coders. For the case of two coders, a relative displacement of the intra-coding mode between the coders is shown to give improved robustness to packet loss. The optimal displacement of the intra-coding mode is found analytically, using a distortion minimization formulation where two independent Gilbert channels are assumed. The analytical results are confirmed by simulations. Tests with an H.263 coder show significant improvement in YPSNR over equivalent systems with no relative displacement of the intra-coding operation.

A real-time implementation and the related theory of a visual-aided inertial navigation system are presented. The entire system runs on a standard laptop with off-the-shelf sensory equipment connected via standard interfaces. The visual-aiding is based on epipolar constraints derived from a finite visual memory. The navigational states are estimated with a squareroot sigma-point Kalman filter. An adaptive visual memory based on statistical coupling is presented and used to store and discard images selectively. Timing and temporal ordering of sensory data are estimated recursively. The computational cost and complexity of the system is described, and the implementation is discussed in terms of code structure, external libraries, and important parameters. Finally, limited performance evaluation results of the system are presented.

The emergence of global navigation satellite systems (GNSSs) has enabled tremendous development in vehicular navigation for various applications. The GNSS technology provides a unique global positioning capability with meter-level accuracy at a low hardware cost and zero marginal infrastructure cost. The GNSSs work by using the satellites as radio beacons, broadcasting a satellite-specific signal and their own position. The range to the satellites is measured up to a common clock offset, and any user equipped with a GNSS receiver capable of receiving the signal from four or more satellites can position itself by multilateration. The position, being a fundamental piece of information for automatizing and facilitating location-dependent system interaction and services, makes the GNSS an enabling technology for many intelligent vehicle and transportation system capabilities.

This chapter will focus on introducing the basic principles of the GNSS technology and the signal processing that allows the GNSS receiver to determine its position: in>Sect. 1, the technology, its limitations, and currently available GNSSs are reviewed; in >Sect. 2, the principles of the GNSS positioning, the signal characteristics, and fundamental components are discussed; in>Sect. 3, the theoretical relations governing the positioning are presented; in>Sect. 4, implementation-related issues, error sources, and GNSS receivers are discussed; in>Sect. 5, the method of differential GNSS is introduced and current augmentation systems are reviewed; and finally in>Sect. 6, conclusions are drawn and references, for further reading about different aspects of the GNSS technology, are given.

The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.

In this paper, an ego-motion estimation approach is introduced that fuses visual and inertial information, using a monocular camera and an inertial measurement unit. The system maintains a set of feature points that are observed on the ground plane. Based on matched feature points between the current and previous images, a novel measurement model is introduced that imposes visual constraints on the inertial navigation system to perform 6 DoF motion estimation. Furthermore, feature points are used to impose epipolar constraints on the estimated motion between current and past images. Pose estimation is formulated implicitly in a state-space framework and is performed by a Sigma-Point Kalman filter. The presented experiments, conducted in an indoor scenario with real data, indicate the ability of the proposed method to perform accurate 6 DoF pose estimation.

In this paper, a novel method for estimating the transformation between an inertial measurement unit (IMU) and a camera together with the intrinsic parameters of the camera is proposed. The method relies on images of reflected feature points in a planar mirror captured by an uncalibrated camera mounted with an IMU. It does not rely on using a fixed calibration pattern in front of the moving camera and the motion is not limited to be planar in front of the mirror. Instead, known feature points located on the camera body are tracked over the time to estimate the IMU-camera transformation and camera intrinsic parameters. A state-space model of the system is derived and then used as input to the Sigma-Point Kalman filter framework. Simulation results show accurate estimation of both IMU-camera translation and rotation parameters as well as the camera intrinsic parameters.

A method is proposed to fuse the information from two navigation systems whose relative position is unknown, but where there exists an upper limit on how far apart the two systems can be. The proposed information fusion method is applied to a scenario in which a pedestrian is equipped with two foot-mounted zero-velocity-aided inertial navigation systems; one system on each foot. The performance of the method is studied using experimental data. The results show that the method has the capability to significantly improve the navigation performance when compared to using two uncoupled foot-mounted systems.

In a compressed sensing setup with jointly sparse, correlated data,we develop a distributed greedy algorithm called distributed predic-tive subspace pursuit. Based on estimates from neighboring sensornodes, this algorithm operates iteratively in two steps: first forminga prediction of the signal and then solving the compressed sensingproblem with an iterative linear minimum mean squared estimator.Through simulations we show that the algorithm provides better per-formance than current state-of-the-art algorithms.

Progressive developments in computing and sensor technologies during the past decades have enabled the formulation of increasingly advanced problems in statistical inference and signal processing. The thesis is concerned with statistical estimation methods, and is divided into three parts with focus on two different areas: sensor fusion and sparse signal processing.

The first part introduces the well-established Bayesian, Fisherian and least-squares estimation frameworks, and derives new estimators. Specifically, the Bayesian framework is applied in two different classes of estimation problems: scenarios in which (i) the signal covariances themselves are subject to uncertainties, and (ii) distance bounds are used as side information. Applications include localization, tracking and channel estimation.

The second part is concerned with the extraction of useful information from multiple sensors by exploiting their joint properties. Two sensor configurations are considered here: (i) a monocular camera and an inertial measurement unit, and (ii) an array of passive receivers. New estimators are developed with applications that include inertial navigation, source localization and multiple waveform estimation.

The third part is concerned with signals that have sparse representations. Two problems are considered: (i) spectral estimation of signals with power concentrated to a small number of frequencies,and (ii) estimation of sparse signals that are observed by few samples, including scenarios in which they are linearly underdetermined. New estimators are developed with applications that include spectral analysis, magnetic resonance imaging and array processing.

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able to incorporate sequential predictions, thereby providing better compressive sensing recovery performance, but not at the cost of high complexity. Through experimental evaluations, we observe that the new algorithm exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.

This paper considers the problem of reconstructing low-rank matrices from undersampled measurements, when the matrix has a known linear structure. Based on the iterative reweighted least-squares approach, we develop an algorithm that exploits the linear structure in an efficient way that allows for reconstruction in highly undersampled scenarios. The method also enables inferring an appropriate regularization parameter value from the observations. The performance of the method is tested in a missing data recovery problem.

In this paper, we consider the schedule-based network localization concept, which does not requiresynchronization among nodes and does not involve communication overhead. The concept makesuse of a common transmission sequence, which enables each node to perform self-localization andto localize the entire network, based on noisy propagation-time measurements. We formulate theschedule-based localization problem as an estimation problem in a Bayesian framework. This pro-vides robustness with respect to uncertainty in such system parameters as anchor locations and timing devices. Moreover, we derive a sequential approximate maximum a posteriori (AMAP) estimator.The estimator is fully decentralized and copes with varying noise levels. By studying the fundamentalconstraints given by the considered measurement model, we provide a system design methodology which enables a scalable solution. Finally, we evaluate the performance of the proposed AMAPestimator by numerical simulations emulating an impulse-radio ultra-wideband (IR-UWB) wireless network.

We investigate a wireless network localization scenario in which the need for synchronized nodes is avoided. It consists of a set of fixed anchor nodes transmitting according to a given sequence and a self-localizing receiver node. The setup can accommodate additional nodes with unknown positions participating in the sequence. We propose a localization method which is robust with respect to uncertainty of the anchor positions and other system parameters. Further, we investigate the Cramer-Rao bound for the considered problem and show through numerical simulations that the proposed method attains the bound.

Due to the rapid error growth of navigation systems using low-cost inertial measurement units there is a need to fuse the information with complementary sensors. In this paper a monocular camera is used to aid the system. Unlike SLAM-like approaches the problem of estimating the location of each feature point viewed in a scene is avoided, instead estimated epipolar points on the image plane are used. By maintaining a buffer of past views, the method mimics a short-term visual memory which imposes multiple constraints on the estimation problem. The result is a Sigma-Point Kalman filter in square-root form with a linear and efficient time-update. A simulation study is presented indicating the filter's capacity to constrain the rate of error growth of an inertial navigation system. The filter may also find useful applications when fusing with additional sensors.

We present a navigation system based on a monocular camera and an inertial measurement unit. The system detects visual tags and fuses the measurements on the image plane with inertial signals to perform pose estimation and localization using a Sigma-Point Kalman filter. The tags are detected by edge-based feature extraction and channel codes. During periods in which tags are not visible, epipolar constraints, arising from past views, are exploited to significantly reduce the position error growth rate. The experimental results in an office building indicate capabilities for indoor navigation.

An estimation procedure for calibration of a low-cost inertial measurement unit (IMU), using a rigidly mounted monocular camera, is presented. The parameters of a sensor model that captures misalignments, scale and offset errors are estimated jointly with the IMU-camera coordinate transformation parameters using a recursive Sigma-Point Kalman Filter. The method requires only a simple visual calibration pattern. A simulation study indicates the filter's ability to reach subcentimeter and subdegree accuracy.

For small-scale Unmanned Aerial Vehicles (UAV) to operate indoor, in urban canyons or other scenarios where signals from global navigation satellite systems are denied or impaired, alternative estimation and control strategies must be applied. In this paper a system is proposed that estimates the self-motion and wind velocity by fusing information from airspeed sensors, an inertial measurement unit (IMU) and a monocular camera. Such estimates can be used in control systems for managing wind disturbances or chemical plume based tracking strategies. Simulation results indicate that while the inertial dead-reckoning process is subject to drift, the system is capable of separating the self-motion and wind velocity from the airspeed information.

For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cramer-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.

The Capon method is a powerful nonparametric approach in array processing based on the sample covariance matrix. For small sample sets, however, its performance is degraded. In this paper we formulate a regularized covariance matching framework based on the nuclear norm for enhancing the Capon method. An approximate iterative solution is developed and tested using simulated data. Appropriate regularization parameter values are also inferred from the data, drawing upon the cross-validation approach. The results show significantly improved spatial spectral and signal waveform estimates.

For compressive sensing of dynamic sparse signals, we develop an iterative greedy search algorithm based on subspace pursuit (SP) that can incorporate sequential predictions, thereby taking advantage of its low complexity while improving recovery performance by exploiting correlations described by a state space model. The algorithm, which we call dynamic subspace pursuit (DSP), is presented and experimentally validated. It exhibits a graceful degradation at deteriorating signal conditions while capable of yielding substantial performance gains as conditions improve.

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE) estimate of the state is given by the conditional mean. Since finding the conditional mean requires multidimensional integration, an approximate MMSE estimator is proposed. The performance of the proposed estimator is evaluated in a positioning problem. Finally, the application of the estimator in inequality constrained recursive filtering is illustrated by applying the estimator to a dead-reckoning problem. The MSE of the estimator is compared with two related posterior Cramer-Rao bounds.

For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori knowledge of matrix structure. In particular, we consider linearly structured matrices, such as Hankel and Toeplitz, as well as positive semidefinite matrices. The performance of the algorithm, referred to as alternating least-squares (ALS), is evaluated by simulations and compared to the Cramer-Rao bounds.

For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises distribution that can parameterize the entire range of prior certainty of the frequencies. An efficient alternating projections method is used to solve the resulting optimization problem. The estimator is evaluated numerically and compared with other estimators and the Cramer-Rao bound.

Pedestrian Dead-Reckoning (PDR) and Radio Frequency (RF) ranging/positioning are complementary techniques for position estimation but they usually locate different points in the body (RF in the head/hand and PDR in the foot). We propose to fuse the information from both navigation points using a constraint filter with an upper bound in the distance between the estimated positions of both sensors.